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Geometrically Nonlinear Analyses of Isotropic and Laminated Shells by a Hierarchical Quadrature Element Method 认领 引用
1
作者 Yingying Lan Bo Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2026年第1期345-373,共29页
In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress res... In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems. 展开更多
关键词 Geometrically exact shell hierarchical quadrature element method geometrically nonlinear laminated shells local p-refinement shear and membrane locking post-buckling behaviors
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Lateral vibration and vibration control methods for ultra-deep well drill strings based on Cosserat geometrically exact beam theory 认领 引用
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作者 Fan Yu Yun-Hu Lu +4 位作者 Yan Jin Wei Li Bing-Qian Lv Hong-Jian Ni Gen-Lu Huang 《Petroleum Science》 SCIE EI CAS CSCD 2026年第5期2655-2685,共31页
In ultra-deep well operations,severe lateral vibration of drill string is a major factorin tool failure and decreased drilling efficiency.To investigate the vibration mechanisms and identify effective mitigation appro... In ultra-deep well operations,severe lateral vibration of drill string is a major factorin tool failure and decreased drilling efficiency.To investigate the vibration mechanisms and identify effective mitigation approaches,a dynamic model for lateral vibration in ultra-deep well drill strings was established using Cosserat geometrically exact beam theory.The model systematically examined the effects of rotational speed,WoB,andstabilizer position andsize on the vibration behavior.Key findings were validated against downhole measurement data from ultra-deep wells.Additionally,two control strategies leveraging modal competition and transverse wave disturbance were proposed.Results indicate that the bottom hole assembly(BHA)is particularly prone tointense lateral vibrations,with its vibrational modes governed by rotational speedand WOB.When the WOB isbelow the critical bucklingload,increasing either the rotational speed or WOBpromotes backward whirling of the BHA,thereby intensifying the vibration severity and bending stress.Conversely,when theWOB exceeds the critical buckling load,the system transitions into a buckling-whirling competition mode,resulting in a significant reduction in the vibration intensityand bending stress.This trend was reasonably verified through field data.Artificially inducingthis low-risk modal competition by adjusting theWOB and rotational speed can effectively reduce the probabilityof drill stringfailure.The motion of stabilizers shifts from forward whirling to backward whirling as the diameter decreases,which considerably alters the vibration-propagation patterns.The vibration-damping effects of both full-gauge and under-gauge stabilizers initially increase and then decrease as their installation position moves upward.Undergauge stabilizers exhibit less consistent behavior under non-severe vibration conditions;nevertheless,they can suppress severe whirling by interfering with adjacent drill string vibrations through lowfrequency transverse waves.They also demonstrate lower sensitivity to the installation position and enhance drill string safety through stress dispersion.Considering comprehensive vibration suppression,drill string integrity,and engineering applicability,installing under-gauge stabilizers can be a viable BHA optimization measure with significant practical value.This study provides a theoretical basis for vibration control in ultra-deep well drill strings,and the proposedstrategy offers valuable insights for improvingdrilling efficiency and ensuring operational safety. 展开更多
关键词 Drill string dynamics Geometrically exact beam Ultra-deep well Lateral vibration Vibration suppression
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A mesoscale numerical study on the geometrically necessary dislocations at grain boundaries and the back stress in polycrystalline grains 认领 引用
3
作者 Tao Zhang Shuang Xu +2 位作者 Xin Lai Lisheng Liu Maoyuan Jiang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第3期258-273,共16页
Elucidating the relationship between geometrically necessary dislocations(GNDs)and back stress is essential for modeling the strain hardening behavior of polycrystalline materials.This study employs dislocation dynami... Elucidating the relationship between geometrically necessary dislocations(GNDs)and back stress is essential for modeling the strain hardening behavior of polycrystalline materials.This study employs dislocation dynamics simulations to quantitatively assess the impact of GND distributions on the associated back stress at the mesoscale.In a simple cubic lattice,the stress fields generated by elementary GND boundaries,including variations in boundary sizes,dislocation types,and distribution patterns,are systematically analyzed.By taking into account the fluctuation of surface GND density,the calculation of back stress is established using the elasticity theory of dislocations combined with scaling functions.It has been demonstrated that the surface GND density is a critical parameter that controls the amplitude of back stress.Subsequently,the prediction of back stress in face-centered cubic crystalline grains is validated with more realistic GND distributions.Considering identical initial Frank-Read sources,dislocation pile-ups are predominantly formed in coarse grains,yet the resulting surface GND density remains comparable to that observed in smaller grains.This phenomenon is responsible for the similar back stress values in grains of varying sizes.Finally,the activation of cross-slip inhibits the formation of dislocation pile-ups,leading to a linear decrease in back stress with increasing plastic strain. 展开更多
关键词 Geometrically necessary dislocations Back stress Dislocation dynamics simulations Elasticity theory of dislocations
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A Shell Element Based on SE(3)Group with Precision-Reserved Interpolation for Geometrically Nonlinear Problems 认领 引用
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作者 Xinyang Ge Yancong Wang +1 位作者 Tiantian Tang Kai Luo 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2026年第3期298-315,共18页
Based on the special Euclidean group SE(3),a geometrically exact shell element is proposed for the analysis of structures undergoing large deformation and finite rotation.First,a unified description of the nodal varia... Based on the special Euclidean group SE(3),a geometrically exact shell element is proposed for the analysis of structures undergoing large deformation and finite rotation.First,a unified description of the nodal variables is established within the SE(3)framework,which accurately captures the coupling effect of translation and rotation.However,conventional interpolation schemes on the non-commutative manifold are path-dependent and fail to maintain physical objectivity,which often leads to spurious strain energy.By combining implicit iterative interpolation and explicit relative configuration interpolation,a precision-reserved interpolation scheme is proposed.By applying the logarithmic mapping on the SE(3)manifold,nodal configuration increments are transformed into the left tangent space of the same reference point,eliminating path dependency.Subsequently,the Lagrange interpolation is applied to both the translational and rotational increments in this tangent space,ensuring their C continuity.Finally,the explicit expressions for the discrete deformation gradients and strains are derived based on the variational principles.Furthermore,the permutation tensor is utilized to handle the variation and linearization of the involved nonlinear mappings.It results in the explicit expression for the geometric stiffness matrix and thus reduces the updating operation of the Jacobian matrix during iterations.Four numerical examples are presented to verify the property of the element in resisting shear locking and its accuracy in handling geometric nonlinear problems of thin-walled or thick-walled structures. 展开更多
关键词 Special Euclidean Group Geometric nonlinearity Locking resistance Relative configuration increment interpolation
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Level-Set-Based Topology Optimization of a Geometrically Nonlinear Structure Considering Thermo-mechanical Coupling Effect 认领 引用 被引量：1
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作者 Sujun Wang An Xu Ruohong Zhao 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2025年第1期100-114,共15页
This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element couplin... This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings. 展开更多
关键词 Topology optimization Geometric nonlinearity Thermo-mechanical coupling effect Level set method Multiple constraints
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Residual elastic stress strain field and geometrically necessary dislocation density distribution around nano-indentation in TA15 titanium alloy 认领 引用 被引量：11
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作者 何东 朱景川 +3 位作者 来忠红 刘勇 杨夏炜 农智升 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2013年第1期7-13,共7页
Nanoindentation and high resolution electron backscatter diffraction（EBSD） were combined to examine the elastic modulus and hardness of α and β phases,anisotropy in residual elastic stress strain fields and distri... Nanoindentation and high resolution electron backscatter diffraction（EBSD） were combined to examine the elastic modulus and hardness of α and β phases,anisotropy in residual elastic stress strain fields and distributions of geometrically necessary dislocation（GND） density around the indentations within TA15 titanium alloy.The nano-indention tests were conducted on α and β phases,respectively.The residual stress strain fields surrounding the indentation were calculated through crosscorrelation method from recorded patterns.The GND density distribution around the indentation was calculated based on the strain gradient theories to reveal the micro-mechanism of plastic deformation.The results indicate that the elastic modulus and hardness for α p hase are 129.05 GPas and 6.44 GPa,while for β phase,their values are 109.80 GPa and 4.29 GPa,respectively.The residual Mises stress distribution around the indentation is relatively heterogeneous and significantly influenced by neighboring soft β phase.The region with low residual stress around the indentation is accompanied with markedly high a type and prismatic-GND density. 展开更多
关键词 nano-hardness stress strain fields geometrically necessary dislocation nanoindentation electron backscatter diffraction TA15 titanium alloy
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GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION 认领 引用 被引量：11
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作者 Xiaofeng Wang Qingshan Yang 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第1期64-72,共9页
Based on the theory of Timoshenko and thin-walled beams,a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper,in which several factors are included such as ... Based on the theory of Timoshenko and thin-walled beams,a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper,in which several factors are included such as lateral shear deformation,warp generated by nonuni-form torsion and second-order shear stress,coupling of flexure and torsion,and large displacement with small strain.With an additional internal node in the element,the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian(UL)formulation.Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams. 展开更多
关键词 spatial beams thin-walled structures geometrically nonlinear finite element stiffness matrix
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Geometrically Exact Finite Element Formulation for Tendon-Driven Continuum Robots 认领 引用 被引量：3
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作者 Xin Li Wenkai Yu +4 位作者 Mehdi Baghaee Changyong Cao Dunyu Chen Ju Liu Hongyan Yuan 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2022年第4期552-570,共19页
Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling c... Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling can be accurate and effective.While for other cases,such as soft robots or robot-environment interactions,the constant curvature assumption can be inaccurate.To model the complex deformation of continuum robots,the geometrically exact beam theory(may also be called the Cosserat rod theory)has been used to develop computational mechanics models.Different from previous computational models that used finite difference schemes for the spatial discretization,here we develop a three-dimensional geometrically exact beam theory-based finite element model for tendon-driven continuum robots.Several numerical examples are presented to show the accuracy,efficiency,and applicability of our new computational model for tendon-driven continuum robots. 展开更多
关键词 Continuum robots Cosserat rod model Geometrically exact beam Finite element method
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Dynamics of slender beam based on geometrically exact Kirchhoff beam theory formulated on SO(3)group 认领 引用 被引量：2
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作者 Zhipeng An Bin Wang +1 位作者 Yunsen Hou Cheng Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2024年第4期212-225,共14页
A geometrically exact Kirchhoff beam formulation(GEKBF)established on the Lie group SO(3)for simulating the dynamics of a slender beam is proposed.The kinematic description,dynamic equilibrium equations and their line... A geometrically exact Kirchhoff beam formulation(GEKBF)established on the Lie group SO(3)for simulating the dynamics of a slender beam is proposed.The kinematic description,dynamic equilibrium equations and their linearization are derived in this framework.Then,a second-order interpolation function for the torsion angle is introduced to improve the convergence of the element.Next,the rotation vector parameterization is developed to reduce the geometric nonlinearity caused by the rotation of the rigid body.In addition,the influence of the reference frame is considered,and the derivation of the elastic force and Jacobian matrix is simplified using the spatial-parallel transport.The semi-discrete equations of motion are in the form of a second-order ordinary differential equation on Lie group,which are solved using the Lie group generalizedα-method.Finally,the accuracy of the proposed formulation is verified using several numerical examples. 展开更多
关键词 Geometrically exact Kirchhoff beam formulation(GEKBF) Slender beam Parallel transport Geometric nonlinearity Large deformation
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Method for Predicting the Fatigue Life of Geometrically Discontinuous Structures Under Combined Bending and Torsion 认领 引用 被引量：2
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作者 Jianhui Liu Xuemei Pan +1 位作者 Yaobing Wei Youliang Wang 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2019年第3期367-377,共11页
The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading.Meanwhile,the application of critical plane method in the prediction of multiaxial fatigu... The fatigue damage model based on theory of damage mechanics is capable of predicting the fatigue life under multiaxial loading.Meanwhile,the application of critical plane method in the prediction of multiaxial fatigue life has made certain progress.According to the law of thermodynamics,a new damage evolution equation is developed in the present study to predict the fatigue life of geometrically discontinuous structure under tension-torsion loading based on damage mechanics and the critical plane method.The essence of this approach is tha t the st rain parame ter of the uniaxial nonlinear fatigue damage model is replaced with the equivalent strain,which consists of the releva nt parame ters of the critical plane.However,it is difficult to calculate the stress-strain status and the critical plane position of geometrically dis?continuous structure by theoretical methods because of the existence of stress concentration and the multiaxial nonproportional characteristics.Therefore,a new numerical simulation method is proposed to determine the critical plane of geometrically discontinuous structure under multiaxial loading by means of the finite element method and MATLAB software.The fatigue life of notched specimens subjected to combined bending and torsion is predicted using the proposed met hod,and the result is compared with t hose from the experimen ts and the Manson-Cfiffin law.The comparisons show that the proposed method is superior to the Manson-Coffin law and is capable of reproducing the experimental results reasonably when the geometry of the structure is complex.It completely meets the needs of engineering practice. 展开更多
关键词 Damage mechanics Critical plane method Geometrically discontinuous structure Finite element method
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Geometrically exact nonlinear analysis of pre-twisted composite rotor blades 认领 引用 被引量：2
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作者 Li'na SHANG Pinqi XIA Dewey H.HODGES 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2018年第2期300-309,共10页
Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the an... Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape,generally anisotropic material behavior and large deflections has been presented based on Hodges＇ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton＇s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade. 展开更多
关键词 Geometrically exact Nonlinear Pre-twisted composite blade Transverse shear deformation Variational asymptotic Warping
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Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg-4Al using in situ tensile testing in scanning electron microscope and HR-EBSD 认领 引用 被引量：2
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作者 Eunji Song Mohsen Taheri Andani Amit Misra 《Journal of Magnesium and Alloys》 SCIE EI CAS CSCD 2024年第5期1815-1829,共15页
In situ tensile testing in a scanning electron microscope(SEM)in conjunction with high-resolution electron backscatter diffraction(HR-EBSD)under load was used to characterize the evolution of geometrically necessary d... In situ tensile testing in a scanning electron microscope(SEM)in conjunction with high-resolution electron backscatter diffraction(HR-EBSD)under load was used to characterize the evolution of geometrically necessary dislocation(GND)densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg-4Al alloy.The increase in GND density was investigated at plastic strains of 0%,0.6%,2.2%,3.3% from the area including 76 grains and correlated with(i)geometric compatibility between slip systems across grain boundaries,and(ii)plastic incompatibility.We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility,from which uniaxial tensile stress-strain response of polycrystalline Mg-4Al are computed and compared with experimental measurement.The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures. 展开更多
关键词 Mg-Al alloys Grain boundaries Geometrically necessary dislocations Strain gradient plasticity HR-EBSD
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Modified unified co-rotational framework with beam,shell and brick elements for geometrically nonlinear analysis 认领 引用 被引量：1
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作者 Yufei Rong Qin Sun Ke Liang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第4期116-127,I0003,共12页
The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis.This paper presents a modified co-ro... The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis.This paper presents a modified co-rotational framework,unified for beam,shell,and brick elements.A unified zero-spin criterion is proposed to specify the local element frame,whose origin is always located at the centroid.Utilizing this criterion,a spin matrix is introduced,and the local frame is invariant to the element nodal ordering.Additionally,the projector matrix is redefined in a more intuitive way,which is the derivative of local co-rotational element frame with respect to the global one.Furthermore,the nodal rotation is obtained with pseudo vector and instantaneous rotation,under a high-order accurate transformation.The resulting formulations are achieved in unified expression and thus a series of linear elements can be embedded into the framework.Several examples are presented to demonstrate the efficiency and accuracy of the proposed framework for large displacement analysis. 展开更多
关键词 Geometrically nonlinear analysis Modified co-rotational framework Unified zero-spin criterion Spin matrix Projector
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REFINED HYBRID MINDLIN PLATE ELEMENT FOR GEOMETRICALLY NON LINEAR ANALYSIS 认领 引用
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作者 郑世杰 陶宝祺 陈万吉 《Transactions of Nanjing University of Aeronautics and Astronautics》 2000年第1期90-94,共5页
Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decompo... Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decomposed into a series of matrices with respect to the assumed strain modes. The formulation presented in this paper is different from any other non linear mixed/hybrid element formulation all successful experience of linear hybrid formulation is absorbed into the formulation(adding non conforming modes and realizing orthogonalization) Numerical results show that the present approach is more effective than any other non linear hybrid element formulation over the accuracy and computational efficiency. In addition, non conforming modes can also overcome the shear locking effect. 展开更多
关键词 non linear mechanics non conforming mode orthogonal approach geometrically non linear refined element
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Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model 认领 引用 被引量：5
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作者 Runqing CAO Zilong GUO +2 位作者 Wei CHEN Huliang DAI Lin WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第2期261-276,共16页
Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid... Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system. 展开更多
关键词 curved pipe conveying fluid pulsating fluid geometrically exact model(GEM) nonlinear dynamics parametric vibration flutter
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A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS 认领 引用 被引量：9
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作者 Xiong Yuanbo Long Shuyao +1 位作者 Hu De＇an Li Guangyao 《Acta Mechanica Solida Sinica》 SCIE EI 2005年第4期348-356,共9页
Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficul... Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate. 展开更多
关键词 local Petrov-Galerkin method moving least square approximation total Lagranian method geometrically nonlinear problems
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LINEAR AND GEOMETRICALLY NONLINEAR ANALYSIS WITH 4-NODE PLANE QUASI-CONFORMING ELEMENT WITH INTERNAL PARAMETERS 认领 引用 被引量：1
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作者 Changsheng Wang Xiangkui Zhang +1 位作者 Ping Hu Zhaohui Qi 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2015年第6期668-681,共14页
A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can ... A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can be applied to nonlinear problems. The weak patch test guarantees the convergence of the element. Then the linear element is extended to the geometri- cally nonlinear analysis in the framework of Total Lagrangian （TL） formulation. The numerical tests indicate that the present element is accurate and insensitive to mesh distortion. 展开更多
关键词 quasi-conforming internal parameters plane element geometrically nonlinear
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Frame-invariance in finite element formulations of geometrically exact rods 认领 引用 被引量：1
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作者 Peinan ZHONG Guojun HUANG Guowei YANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第12期1669-1688,共20页
This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the re... This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm. 展开更多
关键词 geometrically exact rod finite element method interpolation equivariance frame invariance
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Geometrically Nonlinear Topology Optimization of Continuum Structures Based on an Independent Continuous Mapping Method 认领 引用 被引量：11
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作者 Hong-ling Ye Bo-shuai Yuan +2 位作者 Ji-cheng Li Xing Zhang Yun-kang Sui 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2021年第5期658-672,共15页
A geometrically nonlinear topology optimization method for continuum structures is proposed based on the independent continuous mapping method.The stress constraint problem is studied due to the importance of structur... A geometrically nonlinear topology optimization method for continuum structures is proposed based on the independent continuous mapping method.The stress constraint problem is studied due to the importance of structural strength in engineering applications.First,a topology optimization model is established for a lightweight structure with element stress as constraints.Second,the stress globalization method is adopted to convert local stress constraints into strain energy constraints,which overcomes the difficulties caused by local stress constraints,such as model establishment,sensitivity analysis,and massive solution calculations.Third,the sensitivity of the objective function and constraint function is analyzed,and the method of moving asymptotes is employed to solve the optimization model.In addition,the additive hyperelasticity technique is utilized to solve the numerical instability induced by structures undergoing large deformation.Numerical examples are given to validate the feasibility of the proposed method.The method provides a significant reference for geometrically nonlinear optimization design. 展开更多
关键词 Topology optimization Geometric nonlinearity ICM method Stress constraints Stress globalization
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Topology Optimization of Geometrically Nonlinear Structures Under Thermal-Mechanical Coupling 认领 引用 被引量：5
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作者 Boshuai Yuan Hongling Ye +2 位作者 Jicheng Li Nan Wei Yunkang Sui 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2023年第1期22-33,共12页
A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is... A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling. 展开更多
关键词 Topology optimization Geometric nonlinearity Thermal-mechanical coupling Stress constraints
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